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Building free Binary Decision Diagrams using SAT solvers

Wille Robert (Institute of Computer Science at the University of Bremen, Germany)
Fey Görschwin (Institute of Computer Science at the University of Bremen, Germany)
Drechsler Rolf (Institute of Computer Science at the University of Bremen, Germany)

Free Binary Decision Diagrams (FBDDs) are a data structure for the representation of Boolean functions. In contrast to Ordered Binary Decision Diagrams (OBDDs) FBDDs allow different variable orderings along each path. Thus, FBDDs are the more compact representation while most of the properties of OBDDs are kept. However, how to efficiently build small FBDDs for a given function is still an open question. In this work we propose FBDD construction with the help of SAT solvers. "Recording" the single steps of a SAT solver during the search process leads to an FBDD. Furthermore, by exploiting approaches for identifying isomorphic sub-graphs, i.e. cutlines or cutsets reduced FBDDs are constructed.

Keywords: Decision diagrams, Boolean satisfiability, logic synthesis, data structures